 Solution

The predecessor disk block number turns the forward chain into a doubly linked list. Starting from the header's last block, one can traverse backwards; removing or detaching the current block can find its predecessor directly rather than scanning from the beginning. When modifying a chain, the affected predecessor and successor links must both be updated consistently.

The file number identifies the owner of each file data block. A file-system consistency checker can scan the medium, group blocks by owner, detect a cross-link between different files, and help reconstruct chains or headers after damage. It also lets the system check that a block reached through a chain belongs to the expected file.

ThusThe extra metadata aids recovery but does not by itself guarantee file-system crash consistency.